An explicit theory of heights
We consider the problem of explicitly determining the naive height constants for Jacobians of hyperelliptic curves. For genus>1, it is impractical to apply Hilbert's Nullstellensatz directly to the defining equations of the duplication law; we indicate how this technical difficulty can b...
| Main Author: | |
|---|---|
| Format: | Journal article |
| Published: |
1995
|
| _version_ | 1797083202152562688 |
|---|---|
| author | Flynn, E |
| author_facet | Flynn, E |
| author_sort | Flynn, E |
| collection | OXFORD |
| description | We consider the problem of explicitly determining the naive height constants for Jacobians of hyperelliptic curves. For genus>1, it is impractical to apply Hilbert's Nullstellensatz directly to the defining equations of the duplication law; we indicate how this technical difficulty can be overcome by use of isogenies. The height constants are computed in detail for the Jacobian of an arbitrary curve of genus 2, and we apply the technique to compute generators of J(Q), the Mordell-Weil group for a selection of rank 1 examples. |
| first_indexed | 2024-03-07T01:38:21Z |
| format | Journal article |
| id | oxford-uuid:95f8a458-1458-4f51-b26b-b7d268dc2c50 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T01:38:21Z |
| publishDate | 1995 |
| record_format | dspace |
| spelling | oxford-uuid:95f8a458-1458-4f51-b26b-b7d268dc2c502022-03-26T23:49:53ZAn explicit theory of heightsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:95f8a458-1458-4f51-b26b-b7d268dc2c50Mathematical Institute - ePrints1995Flynn, EWe consider the problem of explicitly determining the naive height constants for Jacobians of hyperelliptic curves. For genus>1, it is impractical to apply Hilbert's Nullstellensatz directly to the defining equations of the duplication law; we indicate how this technical difficulty can be overcome by use of isogenies. The height constants are computed in detail for the Jacobian of an arbitrary curve of genus 2, and we apply the technique to compute generators of J(Q), the Mordell-Weil group for a selection of rank 1 examples. |
| spellingShingle | Flynn, E An explicit theory of heights |
| title | An explicit theory of heights |
| title_full | An explicit theory of heights |
| title_fullStr | An explicit theory of heights |
| title_full_unstemmed | An explicit theory of heights |
| title_short | An explicit theory of heights |
| title_sort | explicit theory of heights |
| work_keys_str_mv | AT flynne anexplicittheoryofheights AT flynne explicittheoryofheights |